Question

Spinel is an important class of oxides consisting of two types of metal ions with the oxide ions arranged in ccp layers. The normal spinel has one-eighth of the tetrahedral holes occupied by one type of metal ion and one-half of the octahedral holes occupied by another type of metal ion. Such a spinel is formed by $M{g}^{2+}$ , $A{l}^{3+}$ and $O^{2-}$. The neutrality of the crystal is being maintained.

If oxide ion is replaced by $X^{-8/3}$, the number of anionic vacancies per unit cell is :

• A. $1$
• B. $2$
• C. $3$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

$1$

As $O^{2-}$ ions are at ccp point, spinel has $4$ negative ions in its structure and so, the total positive charge should be $8$.
However, it has $1$ $M{g}^{+2}$ ion occupying one-eight of the tetrahedral holes and $2$ $A{l}^{+3}$ ions occupying one-half of the octahedral holes. So, the compound is $MgA{l}_2{O}_4$.

In a unit cell there are 4 $O^{2-}$ having a total charge of $-8$.
But now, oxide ion is replaced by $X^{-8/3}$ which should have same total negative charge of $-8$ for which only $3$ $X^{-8/3}$ are required. So, one anionic valency will be present in the modified unit cell.
The formula of the new compound is $MgA{l}_2{X}_3$.
Option A is correct.